Animal Spirits, Financial Markets and Aggregate Instability. Wei Dai University of Adelaide. Mark Weder University of Adelaide and CAMA

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1 School of Economics Working Papers ISSN Animal Spirits, Financial Markets and Aggregate Instability Wei Dai University of Adelaide Mark Weder University of Adelaide and CAMA Bo Zhang University of Adelaide Working Paper No May 2017 Copyright the authors

2 Animal Spirits, Financial Markets and Aggregate Instability Wei Dai y The University of Adelaide Mark Weder z The University of Adelaide and CAMA Bo Zhang The University of Adelaide May 23, 2017 Abstract People s animal spirits are a signi cant driver behind the uctuations of the U.S. business cycle. This insight is demonstrated within an estimated arti cial economy with nancial market frictions. Animal spirits shocks account for around 40 percent of output uctuations over the period from 1955 to Financial friction and technology shocks are considerably less important with best point estimates for both near 20 percent. We also nd that the Great Recession, for the most parts, was caused by adverse shocks to expectations. 1 Introduction What are the shocks that cause macroeconomies to experience recurrent sequences of booms and recessions? The current paper attends to this question by presenting evidence on the sources of business cycles for the post-korean War American economy. The results back the view that people s psychological motivations, a.k.a. animal spirits, provoke a signi cant portion of the uctuations in aggregate real economic activity, causing around forty percent of U.S. output volatility. This insight is Keywords: Endogenous nancial frictions, indeterminacy, animal spirits, business cycles, Bayesian estimation. JEL classi cation: E32, E44. y We would like to thank Jess Benhabib, Firmin Doko Tchatoka, Ippei Fujiwara, Nicolas Groshenny, Qazi Haque, Thomas Lubik, Oscar Pavlov, Harald Uhlig, Pengfei Wang, Elliott Weder and Jacob Wong for very helpful comments. Mark Weder acknowledges support from an Australian Research Council research grant (DP ). z Corresponding author: School of Economics, The University of Adelaide, Adelaide SA 5005, Australia (mark.weder@adelaide.edu.au). 1

3 demonstrated within an arti cial economy with nancial market frictions. Likewise, our exercise suggests that it was chie y adverse shocks to expectations that led to the Great Recession. Models with credit market frictions have become popular since the Great Recession and this interest re ects the notion that disruptions to nancial markets were the key factors behind this contraction. Building on earlier work, such as Kiyotaki and Moore (1997) as well as Bernanke, Gertler and Gilchrist (1999), this research has shown how nancial market frictions can amplify shocks to macroeconomic fundamentals by transforming small economic disturbances into large business cycles. 1 Del Negro, Giannoni and Schorfheide (2015) as well as Christiano, Eichenbaum and Trabandt (2015), for example, extend New Keynesian models by nancial market frictions to explain some key aspects of the recession U.S. GDP per capita Baa 10 year U.S. government bond Figure 1: U.S. GDP and credit spread (on right-hand scale) at business cycle frequencies. Shaded areas indicated NBER recessions. We depart from the aforementioned works twofold. First, the parametric space of the model includes multiple equilibria such that self-ful lling nonfundamental stochastic shocks to beliefs can act as impulses of endogenous cycles. Second, unlike most existing work on such indeterminacy, the analysis concentrates on estimating the model and focuses on the empirical implications of the multiplicity by explicitly analyzing the business cycle variance contribution of animal spirits or belief shocks. The undertaking is implemented by building on a variant of Benhabib and Wang (2013). 2 Indeterminacy in this model is linked to the empirically observed countercyclical movement of nancial market tightness. Figure 1 plots the pattern of nancial market health and aggregate economic activity. Financial health is instrumented by the Baa Corporate Bond Spread which is displayed on an inverted scale and opposite the uctuations of per capita GDP. The shaded areas in the gure correspond to NBER recessions. They highlight that nancial conditions are countercyclical and deteriorate markedly during most slumps. 1 See also Nolan and Thoenissen (2009). 2 Azariadis, Kaas and Wen (2016) and Harrison and Weder (2013) are other examples that combine multiple equilibria and nancial frictions. 2

4 In the arti cial economy, the interaction of a time varying collateral constraint and a countercyclical markup spawns equilibrium indeterminacy, a condition that allows aggregate uctuations to be caused by extrinsic changes to people s expectations. Moreover, in addition to such animal spirits shocks, the economy is bu eted by a parade of fundamental shocks. The model is estimated by full information Bayesian methods using quarterly U.S. data covering the period from 1955:I to 2014:IV. This approach follows various key contributions by Otrok (2001), Justiniano, Primiceri and Tambalotti (2011) as well as Schmitt-Grohé and Uribe (2012), who all, however, only explore the role of fundamental shocks as the engines of business cycles. The Bayesian estimation chooses disturbances so that the probability of empirical series (i.e. the observables) is maximized and the key result that ensues from this exercise is that animal spirits are important drivers of the repeated uctuations of the U.S. macroeconomy. Speci cally, by computing forecast error variance decompositions, we nd that animal spirits account for about forty percent of U.S. output variations and for about two thirds of the uctuations in investment. Disturbances that originate in the nancial sector explain less than ten percent of output uctuations. Moreover, historical decomposition of output growth shows that belief shocks have decidedly (although not exclusively) contributed to the sharp contraction in economic activity of the Great Recession that began at the end of Previous work on multiple equilibria economies has overwhelmingly remained in the theoretical realm and estimation exercises have been rare. Farmer and Guo (1995) is an early attempt to estimate a (real) sunspot model using classical simultaneous equations methods. Pintus, Wen and Xing (2016) and Pavlov and Weder (2017) perform full-information Bayesian estimations as in the present paper. While Pintus, Wen and Xing build a model with nancial market frictions, they do not establish a signi cant role for animal spirits. Financial markets are not featured in Pavlov and Weder and their study purposely excludes the Great Recession. 2 The Model The arti cial economy is a discrete-time adaptation of Benhabib and Wang (2013). The model features credit frictions in the form of endogenous borrowing constraints in a model of monopolistic competition in which, as usual, perfectly competitive rms produce nal output by combining a continuum of di erentiated intermediate inputs. Intermediate goods producing rms are collateral-constrained in how much they can borrow to nance their working capital needs. We modify the original model by incorporating a set of fundamental shocks which are frequently considered as key drivers of business cycles. The model s discussion will be relatively brief and it will concentrate on the alterations from the original setup. 2.1 Technology A unit mass of monopolistic competitive rms has access to a constant returns technology that transforms capital services t (i) and labor hours N t (i) into interme- 3

5 diate, di erentiated outputs Y t (i) Y t (i) = t (i) (X t N t (i)) 1 0 < < 1: Exogenous labor-augmenting technological progress X t a ects all rms equally. Its growth rate x t X t =X t 1 evolves as a rst-order autoregressive process ln x t = (1 x ) ln x + x ln x t 1 + " x;t 0 < x < 1 with " x;t v N(0; 2 x) and ln x is average growth rate. The rms rent factor services from the households at perfectly competitive prices W t and r t. Final output Y t is a constant elasticity of substitution aggregator of a basket of intermediate inputs Z 1 Y t = 0 Y t (i) 1 1 di > 1: Here denotes the elasticity of substitution between varieties. The monopolistic competitive rms generate pro ts by charging a mark-up over marginal costs. They must borrow for working capital needs. Imperfect enforcement requires a process to constrain borrowing by the value of the collateral. Speci cally, rm i s total amount of debt is an intraperiod loan B t (i) B t (i) = W t N t (i) + r t t (i) and it is constrained by the value of the collateral, which is the output being produced, i.e. W t N t (i) + r t t (i) t t P t (i)y t (i): Under this credit constraint, if there is a default event, the lender has the right to recover a fraction of less than one of the rm s end-of-period value of output P t (i)y t (i). 3 The model features two nancial frictions and their product t t represents the arti cial economy s nancial tightness. Concretely, t refers to an endogenous credit constraint: the borrowing constrictions vary with the aggregate state of economic activity which re ects creditors ability to pay back loans. In particular, t is an increasing function of the deviation of actual from balanced growth output t = Yt with the parameter restrictions 0 < < 1 and > 0. The parsimonious formulation of t entails many micro-founded makeups without the need to con ne itself to a particular one. For example, it can stand in for Benhabib and Wang s (2013) original setup with xed liquidation costs. In addition to the endogenous component, 3 Unlike the original model, our setup does not include xed liquidation costs. Indeterminacy still holds. When we compare the two models using Bayesian estimation method, we nd that the model without xed costs is favored by the data. Y t 4

6 exogenous disturbances t a ect nancial health. These shocks originate in the nancial sector as in Jermann and Quadrini (2012) and Liu, Wang and Zha (2013). The collateral or nancial shock t evolves as ln t = (1 ) ln + ln t 1 + " ;t 0 < < 1 with " ;t v N(0; 2 ) and steady state value = 1. The corresponding rst-order conditions for the pro t maximization problem involve and r t t (i) = t Y t (i) W t N t (i) = (1 ) t Y t (i) 1 P 1 t(i) t + t (i) t t P t(i) t = 0 (1) where t stands for monopolistic rms marginal costs and t (i) denotes the multiplier associated with the borrowing constraint. 2.2 Preferences Households are represented by an agent with the lifetime utility E 0 1 X t=0 t ln(c t t ) ' N 1+ t < < 1; 0 and ' > 0 where is the discount factor, C t stands for consumption, and N t for total hours worked. The functional form of the period utility ensures that the economy is consistent with balanced growth. The parameter ' denotes the disutility of working. The term t represents shocks to the agent s utility of consumption that generate urges to consume, as in Baxter and King (1991) and Weder (2006). The preference shock follows the autoregressive process ln t = ln t 1 + " ;t 0 < < 1 with " ;t v N(0; 2 ). This shock is also a driver of the economy s labor wedge, i.e. the gap between the marginal rate of consumption-leisure substitution and the marginal product of labor. Hence, our estimation will allow a much wider interpretation than mere shocks to preferences a more agnostic reading includes, for example, changes to monetary policy, taxes, or labor market frictions. Households own the physical capital stock K t and decide on its utilization rate, u t, thus t = u t K t. The agent faces the period budget constraint and the law of motion for capital is C t + A t I t + T t = W t N t + r t u t K t + t K t+1 = (1 t )K t + I t : 5

7 The term I t is investment spending and A t represents a non-stationary investmentspeci c technology shock which a ects the transformation of consumption goods into investment goods. In the model, the concept corresponds to the relative price of new investment goods in terms of consumption goods. The shock s growth rate a t evolves as ln a t = (1 a ) ln a + a ln a t 1 + " a;t 0 < a < 1 with " a;t v N(0; 2 a), and ln a is the average growth rate. Lump-sum taxes are denoted by T t. The rate of physical capital depreciation u 1+ t t = < 0 < 1 and > 0 is an increasing function in the utilization and > 0 measures the elasticity of the depreciation rate with respect to capacity used. The rst-order conditions are standard and delegated to the Appendix. 2.3 Government The government purchases G t units of the nal output. G t is neither productive nor does it provide any utility. The spending is nanced by the lump-sum taxes. We model government s spending with a stochastic trend X G t = (X G t 1) yg (X Y t 1) 1 yg 0 < yg < 1 where yg governs the smoothness of the government spending trend relative to the trend in output. Then, detrended government spending is g t G t =X G t and this follows the process with the shock s variance 2 g. 2.4 Equilibrium ln g t = (1 g ) ln g + g ln g t 1 + " g;t 0 g < 1 In symmetric equilibrium, t (i) = u t K t, N t (i) = N t, P t (i) = P t = 1, Y t (i) = Y t and t (i) = t = Y t W t N t r t u t K t, hold and (1) becomes 1 t + t t t 1 t = 0: (2) 1 From (2), and if t t < t < 1, the nancial constraint binds, thus, t = t t = t Yt Y t : In the steady state, equals marginal costs thus it is not a free parameter. 6

8 Elasticity of collateral ( ) 2.5 Self-ful lling dynamics The self-ful lling prophecy is, in the beginning, a false de nition of the situation evoking a new behavior which makes the originally false conception come true. [Merton, 1948] The detrended and linearized economy is solved numerically (using standard parameters as listed in Table 1). We assume that the credit constraint is always binding. Figure 2 maps the local dynamics zones in the 1 space. If market power is small, i.e. the inverse of the marginal cost 1 is close to one and the credit limit is constant, i.e. the curvature parameter is small, the economy s dynamics are unique. However, combinations of market power and a procyclical credit limit delivers indeterminacy. The indeterminacy mechanism operates via an upwardly sloping wage-hours locus similar to many animal spirits models. 4 Then, how can pessimistic expectations about the future create problems? If people believe that the future is worse, they will attempt to work more hours. In terms of the labor market equilibrium, this change in expectations will shift the labor supply curve out. But the pessimistic expectations will lead households to decrease the lending to rms. This contraction of credit will tighten the rms borrowing constraints; costs and markups will rise and the individual labor demand schedules move leftwards. As a consequence, the economy s wage-hours-locus is upwardly sloping. In equilibrium, the outward shift of labor supply will result in lower employment and in a drop in aggregate production, in sum, the low animal spirits will be self-ful lling Determinacy Source Indeterminacy (degree=1) 0.2 Determinacy Figure 2: Parameter space for dynamics. 3 Estimation The arti cial economy s local dynamics can become indeterminate. Our next step is to discuss how animal spirits are introduced into the model, to present the data that is employed in the analysis, as well as to outline the full information Bayesian estimation of the arti cial economy. Finally, we compare the estimated shocks to corresponding empirical measures. 4 See for example, Farmer and Guo (1994) or Wen (1998). 7

9 If there are many rational expectations equilibria in the model economy, this continuum is a device to introduce animal spirits. To do this, we break down the forecast error of output y t ^y t E t 1^y t into fundamental and non-fundamental components, as suggested by Lubik and Schorfheide (2003): y t = x " x t + a " a t + " t + g " g t + " t + " b t: The parameters x, a,, g and determine the e ect of technological progress, investment-speci c technology, preferences, government spending and collateral shocks on the expectations error. This break-down leaves the belief shock " b t as a residual. The last equation promulgates a strict de nition of animal spirits: they are orthogonal to the other disturbances, thus independent of economic fundamentals. We now estimate the model, allowing all six shocks to matter. The approach attributes the contribution of each shock to aggregate uctuations. The estimation uses quarterly U.S. data running from 1955:I to 2014:IV and includes seven observable time series: (i) the log di erence of real per capita GDP, (ii) real per capita consumption, (iii) real per capita investment, (iv) real per capita government spending, (v) the relative price of investment, (vi) the log di erence of per capita hours worked from its sample mean, as well as (vii) the credit spread from its sample mean. We instrument nancial market conditions by a credit spread similar to Christiano, Motto and Rostagno (2014). In particular, Christiano, Motto and Rostagno make use of the di erence between the interest rate on Baa corporate bonds and the ten-year US government bond rate. The Appendix provides a full description of the data and its construction. The corresponding measurement equation is ln Y t ln Y t 1 ln C t ln C t 1 ln A t I t ln A t 1 I t 1 ln G t ln G t 1 ln A t ln A t 1 ln N t ln N credit spread 3 2 = ^y t ^y t 1 + ^ y t ^c t ^c t 1 + ^ y t ^{ t ^{ t 1 + ^ y t ^g t ^g t 1 + ^a g t ^a g t 1 + ^ y t ^ a t ^N t x ^ t ln y ln y ln y ln y ln a where a g t Xt G =Xt Y = (a g yg t 1) ( y t ) 1. In the last measurement equation, x is the scale parameter only appearing in the measurement equation to adjust the di erence of the volatilities (that is, units) between the model frictions and the observable variable. Both output growth and credit spread are measured with errors " me y;t and " me s;t which are i.i.d. innovations with mean zero and standard deviation me y and me s, respectively. Allowing for a measurement error to output is a way to circumvent stochastic singularity (e.g. Schmitt-Grohé and Uribe, 2012). A measurement error to the spread can account for any mis-measurement in the data, especially when only a proxy is observed (e.g. Justiniano, Primiceri, and Tambalotti, 2011). Both measurement errors are restricted to absorb not more than ten percent of the variance of the corresponding observables. " me y;t " me s;t

10 Prior to the estimation, we x a number of parameters. This set of parameters is calibrated following the literature and is based on national accounts data averages. We only address some of these calibrations (all are listed in completion in Table 1). The elasticity of substitution parameter is set at ten, as in Dotsey and King (2005) and Cogley and Sbordone (2008). The average government spending share in GDP, G=Y, is calibrated at 21 percent, a number which we take from national accounts. The quarterly growth rates of per capita output y and the relative price of investment a are set equal to their sample averages of and Finally, the household s rst-order conditions determine the elasticity of the depreciation rate from = ( k = 1)=. The other model parameters are estimated. Our prior assumptions are summarized in Table 2. The parameters estimated here include the steady state marginal cost (or equivalently the inverse of the mark-up), the elasticity of collateral, the scale parameter x, the parameters that describe the stochastic processes and the standard deviation of the measurement error. A beta distribution is adopted for the steady-state marginal cost and its value falls between 0.83 and 0.9, so that the steady-state markup varies from around 11 to 20 percent. The range of marginal costs is chosen for two reasons. First, the empirically estimated markup falls in this range (see for example Cogley and Sbordone, 2008). Second, the upper value of is further restricted by the inequality constraints 1 < < 1 for the nancial constraint to bind. 5 We set the prior mean for x to match the standard deviation of the smoothed endogenous nancial frictions in the model without any nancial information (data and shock) and the standard deviation of the demeaned spread data. We adopt an inverse gamma distribution for the prior. For the persistence parameters we use a beta distribution and the standard deviations of the shocks follow an inverse gamma distribution. The prior distributions for the expectational parameters x, a,, g and are uniform, thus agnostic about their values. Endogenous priors prevent overpredicting the model variances (as in Christiano, Trabandt and Walentin, 2011). We use the Metropolis-Hastings algorithm to obtain one million draws from the posterior for each of the two chains, discard half of the draws, and adjust the scale in the jumping distribution to achieve a percent acceptance rate for each chain. The last two columns of Table 2 present the posterior means of the estimated parameters, along with their 90 percent posterior probability intervals. The parameters are precisely estimated as is evidenced by the percentiles. The estimated steady state of marginal cost implies a steady state markup of twenty percent. Preference, government spending and collateral shocks exhibit a high degree of persistence. The autocorrelation of the non-stationary technology shock is low, but it is not inconsistent with the moderate values commonly found in the literature. Table 3 reports second moments of the main macroeconomic variables calculated 5 To land in the prior region of, we calculate the required region of to generate indeterminacy given each value of, as shown in Figure 1. We choose the minimum value 0.16 as the lower bound of the prior region, while is the upper limit. This range will guarantee that we can cover the complete indeterminacy region. Since our model is indeterminate, during the MCMC, all proposed draws from the determinacy and source regions were discarded. 9

11 using U.S. data and compares these moments to those obtained from model simulations at the posterior mean. The model underpredicts the volatility, but it matches fairly well the relative standard deviations, autocorrelations and the variables crosscorrelations with output. Table 4 displays the contribution of each structural shock, which we list in the rst row, to the variances of key macroeconomic variables. The decomposition suggests that animal spirits shocks " b t are the most important source of U.S. aggregate uctuations. These shocks account for over forty percent of output growth. The Appendix presents a more detailed analysis of the beliefs driven cycle in the spirit of Burns and Mitchell (1946). The other aggregate demand shocks play a lesser role and the contribution of the two technology shocks is small at no more than twenty percent. For investment, the vast majority of its variations comes from animal spirits suggesting that much of the spending is driven by entrepreneurial sentiments. The credit spread (i.e. the nancial frictions) is mainly driven by stochastic nancial factors by about forty percent Growth rates of Fernald's TFP Growth rates of model's TFP Figure 3: Fernald s vs Model s total factor productivity We identify the shocks by estimating in a system and it is thus fair to ask if the shocks are meaningfully labelled. More concretely, do the shocks share resemblance with empirical series that are computed with orthogonal information sets? To begin with, the estimated model s total factor productivity series is compared with Fernald s (2014) total factor productivity series for the United States. 7 Fernald s series are widely considered as the gold standard for this variable for which he adjusts for variations in factor utilization (labor e ort and the workweek of capital) as well as labor skills. The results are reassuring as shown in Figure 3. Both productivity series not only have similar amplitudes, but their contemporaneous correlation comes in at 0:65. Next, Figure 4 compares the index of estimated con dence and the U.S. Business Con dence index (band-pass ltered to concentrate on the relevant frequencies). Clearly, the empirical con dence index is in uenced by a raft of fundamentals and non-fundamentals, thus, it is not exactly clear how the empirical data would map our theoretical notion of animal spirits. Yet, the two con dence series are strongly correlated with coe cient 0:64 and we interpret the relationship in Figure 4 as endorsing 6 We also estimate the model using loan data and animal spirits remain important. 7 Growth of total factor productivity in our model is given by (1 )(^ x t + ln x ): 10

12 our estimation and as supporting the case that estimated shocks re ect variations in people s expectations about the future path of the economy. 8 Furthermore, our estimated disturbances share similarity to Angeletos, Collard and Dellas (2016, Figure 8) con dence shocks. While Angeletos, Collard and Dellas argue in a unique-equilibrium model, we interpret the resemblance as complementary stories of the business cycle Confidence index Belief shocks Figure 4: Business con dence index vs animal sprits shocks (normalized data). 4 Checks of robustness In this section, we consider several robustness checks: (i) Lubik and Schorfheide s (2003) representation of a belief shock is compared to Farmer, Kharamov and Nicolò s (2015) formulation, (ii) we go through alternative observables to measure nancial markets health, (iii) Fernald s (2014) TFP data is added to the observables, and (iv) permanent technology shocks are replaced by transitory shocks. To demonstrate the robustness of the above insights, we follow the approach of Farmer, Khramov, and Nicolò (2015) in which the animals spirits shock is simply the forecast error, i.e. Y t = " s t; with variance 2 : Intuitively, since output is forward looking, this expectation error should be correlated with fundamental shocks. Yet, it is also a sunspot shock, as it can cause movements in economic activity without any shifts to fundamentals. Assuming a uniform distribution, we thus estimate the correlations between Y t and the fundamental shocks. The priors for the other parameters are kept the same as in the baseline model. As can be seen from Tables 2 and 5, our estimation results are robust to the formation of the expectation error. The posterior distributions are almost identical and the closeness of the log-data densities con rms that the goodness of t between the models is equivalent. 9 The next robustness check concerns the choice of the observed spread when instrumenting nancial markets conditions. We thus consider the sensitivity to using various alternative spreads. In particular, we sequentially explore if (i) the Baa-Aaa 8 The correlation of the estimated sunspot shocks and Fernald s TFP series is 0:17. 9 Second moments and variance decompositions are virtually identical and are not presented to conserve space. 11

13 spread, (ii) the Baa-Federal funds rate spread or (iii) the Gilchrist and Zakrajšek s (2012) spread yield signi cantly di erent results in the estimation. We report the variance decompositions only. The results for the Baa-Aaa and Baa-Federal funds rate spreads are reported in Tables 6 and 7. Animal spirits continue to stand out as the main driver of the business cycle. The tables suggest that they account for about 40 percent of the U.S. output uctuations. Only when using Gilchrist and Zakrajšek s (2012) spread do nancial shocks contributions climb to slightly over ten percent. 10 Next, we add total factor productivity to the catalog of observables. Fernald s (2014) continuously updated data is the natural series to choose from. Fernald adjusts for variations in factor utilization (labor and capital) and includes adjustment for quality or composition. Most of these in uences are not part of the arti cial economy and we thus add one more measurement error on total factor productivity (at not more than ten percent). Table 9 shows that the previous results remain robust. Animal spirits continue to cause the bulk of U.S. output uctuations. The technology shocks contributions are lower, with a best point estimate near 10 percent. Finally, we replace permanent technology shocks by transitory shocks. Then, the production technology is given by Y t = Z t K t ( t N t ) 1 and the growth rate of labor augmenting technological progress is deterministic at the constant rate, as in King, Plosser and Rebelo (1988). We permit temporary changes in total factor productivity through Z t, which follows a rst-order autoregressive process ln Z t = (1 z ) ln Z + z ln Z t 1 + " z;t 0 < z < 1: The model estimation delivers similar posterior means of the parameters as the baseline estimation and they are thus not reported here (see Appendix). Noteworthy is, however, the estimate for z at 0:997. While high, this number is consistent with Ireland (2001), for example. The variance decompositions of the stationary technology shocks model are reported in Table 10. Technology shocks account for about 17 percent of GDP volatility. However, animal spirits remain the most critical driver of aggregate uctuations and they continue to explain roughly forty percent of output growth variations. Now, which speci cation of technology is favored by data? This question is answered in Table 11 which compares the model ts of the two alternatively speci ed models. Data strongly prefers a version of the model in which total factor productivity has a stochastic trend. We have conducted further robustness checks that are, however, delegated to the Appendix to conserve space. 5 A closer look at the Great Recession From 2007 to 2009, the U.S. economy was in the turmoil of a severe recession. The Great Recession was the single-worst economic contraction since the 1930s, with 10 However, this change appears to be mainly the outcome of a shorter sample given the spread s availability. To con rm this, we re-estimated the model using the other spreads, but only covering the 1973 to 2014 period. As expected, the results then came out very similar to Table 8 s 12

14 economic activity diving after various nancial institutions collapsed. One of the aims of the recent nancial friction models is to identify the sources of the crisis. We follow this line and look more closely into the years 2007 to Initial values 0.04 Spread M.error 0.02 Output M.error Belief 0 Productivity 0.02 Investment 0.04 Collateral Government Q1 07Q2 07Q3 07Q4 08Q1 08Q2 08Q3 08Q4 09Q1 09Q2 09Q3 09Q4 Figure 5: Historical decomposition of output growth Preference To begin with, we plot in Figure 5 the historical decomposition of the structural shocks to output growth over the 2007:I to 2009:IV period. The gure suggests that it was foremost pessimistic expectations that contracted the economy from the end of 2007 onwards. Thus, the data favors the interpretation that the Great Recession was closely associated with self-ful lling beliefs. Our interpretation of events goes like this: when the run-up of real estate prices came to an end, when banks curbed lending and tightened credit, when investors stopped borrowing, then this occurred because people were expecting worsening business conditions and higher defaults. In other words, people became pessimistic and, as a consequence of the e ect on nancial markets, this pessimism became self-ful lling. Thus, our results do not necessarily contradict Christiano, Eichenbaum and Trabandt s (2015) account of the Great Recession. Their study nds that the steep decline of aggregate economic activity was overwhelmingly caused by (exogenous) nancial frictions. What our analysis suggests is, however, that a sudden drop in people s animal spirits found its catalyst in nancial markets. In this reading of events, the nancial sector propagated gloomy animal spirits into a full-blown nancial crisis and disastrous macroeconomic collapse ensued. Moreover, Brinca, Chari, Kehoe and McGrattan assert that [...] considering the period from 2008 until the end of 2011, [our] results imply that the Great Recession in the United States should be thought of as primarily a labor wedge recession. [Brinca, Chari, Kehoe and McGrattan, 2017, 1042] What does the labor wedge look like in the arti cial economy s benchmark version? The model s labor wedge is driven by uctuations of both the markup as well as stochastic preferences. It is plotted along with the data equivalent in Figure 6. Clearly, the two series show high conformity. The arti cial wedge explains 75 percent of the data wedge s plunge during 2008 and 2009 and it charts a tepid recovery over 13

15 Index (2008:1=100) the 2010 to 2014 period. Thus, to an extent, our model is not inconsistent with Brinca, Chari, Kehoe and McGrattan s (2017) interpretation of the Great Recession Labor wedge (US) Labor wedge (Model) Figure 6: The arti cial labor wedge during the Great Recession. 6 Does data prefer indeterminacy? So far we have restricted the analysis to the parameter space with multiple equilibria, yet a natural question arises: does data in fact favor a model with indeterminacy? To answer this question, we now estimate the economy across the complete area of the parameter space as in Bianchi and Nicolò (2017) 11. Their procedure can be implemented without knowing the boundaries between the four dynamic regions (see Figure 2). During the mode- nding process, the estimation can get stuck in a region without crossing the boundaries, even though, in theory, the Metropolis-Hastings algorithm can explore the entire parameter space. Therefore, our implemented estimation strategy was to set di erent initial values (in all regions) while leaving the priors the same. Once a region-speci c (i.e. local) mode was found, the Markov chain Monte Carlo procedure was run at each mode. The priors are such that indeterminacy has the least prior probability so to err on the right side. To do this, we adjust the prior of the elasticity of collateral, which is now gamma-distributed centered at 0.5 with standard deviation 0.8. The prior for the parameter ' is uniformly distributed within [0,2]. In line with Bianchi and Nicolò (2017), we follow the approach proposed in Farmer, Kharamov and Nicolò (2015) and construe the forecast error of output y t as a belief shock with variance 2 and allow the expectation errors to be correlated with the fundamental shocks (Table 5 reports the equivalence of this setup to our benchmark model). The log data densities in Table 12 suggest that U.S. data strongly favours the indeterminacy model over versions of the economy in which animal spirits do not play a role. 11 The Appendix explains their methodology in more detail. 14

16 7 Concluding remarks This paper has presented evidence on the sources of U.S. aggregate uctuations over the period 1955 to We perform a Bayesian estimation of a nancial accelerator model which features an indeterminacy of rational expectations equilibria. Indeterminacy in the model is linked to the empirically observed countercyclical movement of nancial market tightness. The interaction of time-varying collateral constraints and a countercyclical markup brings about an upwardly sloping wagehours-locus and aggregate uctuations can be driven by changes to people s animal spirits. The arti cial economy is driven both by fundamental shocks as well as by animal spirits and its estimation supports the view that people s animal spirits play a signi cant role for the U.S. business cycle. Moreover, data favours the indeterminacy model over versions of the economy in which sunspots do not play a role. Variance decompositions suggest that animal spirits are behind around forty percent of output growth variations and they explain an even larger portion of uctuations in investment spending. Technology shocks and nancial frictions shocks are signi cantly less important and they explain no more than twenty percent of the oscillations in aggregate real economic activity. The recession appears to have been chie y caused by adverse con dence shocks. References [1] Adelman, F., and I. Adelman (1959): The Dynamic Properties of the Klein- Goldberger Model, Econometrica 27, [2] Angeletos, G.-M., F. Collard and H. Dellas (2016): Quantifying Con dence, University of Bern, mimeo. [3] Azariadis, C., L. Kaas and Y. Wen (2016): Self-Ful lling Credit Cycles, Review of Economic Studies 83, [4] Baxter, M. and R. King (1991): Productive Externalities and Business Cycles, Federal Reserve Bank of Minneapolis, mimeo. [5] Benhabib, J. and P. Wang (2013): Financial Constraints, Endogenous Markups, and Self-ful lling Equilibria, Journal of Monetary Economics 60, [6] Bernanke, B., M. Gertler and S. Gilchrist (1999): The Financial Accelerator in a Quantitative Business Cycle Framework, in: Handbook of Macroeconomics, J. Taylor and M. Woodford (editors), , Elsevier. [7] Bianchi, F. and G. Nicolò (2017): A Generalized Approach to Indeterminacy in Linear Rational Expectations Models, mimeo. [8] Burns, A. and W. Mitchell (1946): Measuring Business Cycles, National Bureau of Economic Research, New York. 15

17 [9] Christiano, L., M. Eichenbaum and M. Trabandt (2015): Understanding the Great Recession, American Economic Journal: Macroeconomics 7, [10] Christiano, L., R. Motto and M. Rostagno (2014): Risk Shocks, American Economic Review 104, [11] Christiano, L., M. Trabandt and K. Walentin (2011): Introducing Financial Frictions and Unemployment into a Small Open Economy Model, Journal of Economic Dynamics and Control 35, [12] Cogley, T. and A. Sbordone (2008): Trend In ation, Indexation, and In ation Persistence in the New Keynesian Phillips Curve, American Economic Review 98, [13] Del Negro, M., M. Giannoni and F. Schorfheide (2015): In ation in the Great Recession and New Keynesian Models, American Economic Journal: Macroeconomics 7, [14] Dotsey, M. and R. King (2005): Implications of State-dependent Pricing for Dynamic Macroeconomic Models, Journal of Monetary Economics 52, [15] Farmer, R., and J.-T. Guo (1994): Real Business Cycles and the Animal Spirits Hypothesis, Journal of Economic Theory 63, [16] Farmer, R., and J.-T. Guo (1995): The Econometrics of Indeterminacy: An Applied Study, Carnegie-Rochester Conference Series on Public Policy 43, [17] Farmer, R., V. Khramov and G. Nicolò (2015): Solving and Estimating Indeterminate DSGE Models, Journal of Economic Dynamics and Control 54, [18] Fernald, J. (2014): A Quarterly, Utilization-adjusted Series on Total Factor Productivity, Federal Reserve Bank of San Francisco, mimeo. [19] Gilchrist, S. and E. Zakrajšek (2012): Credit Spreads and Business Cycle Fluctuations, American Economic Review 102, [20] Greenwood, J., Z. Hercowitz and G. Hu man (1988): Investment, Capacity Utilization, and the Real Business Cycle, American Economic Review 78, [21] Harrison, S. and M. Weder (2013): Sunspots and Credit Frictions, Macroeconomic Dynamics 17, [22] Ireland, P. (2001): Technology Shocks and the Business Cycle: An Empirical Investigation, Journal of Economic Dynamics and Control 25, [23] Jermann, U. and V. Quadrini (2012): Macroeconomic E ects of Financial Shocks, The American Economic Review 102, [24] Justiniano, A., G. Primiceri and A. Tambalotti (2011): Investment Shocks and the Relative Price of Investment, Review of Economic Dynamics 14,

18 [25] King, R. and C. Plosser (1994): Real Business Cycles and the Test of the Adelmans, Journal of Monetary Economics, 33, [26] King, R., C. Plosser and S. Rebelo (1988): Production, Growth and Business Cycles I. The Basic Neoclassical Model, Journal of Monetary Economics 21, [27] Kiyotaki, N. and J. Moore (1997): Credit Cycles, Journal of Political Economy 105, [28] Liu, Z., P. Wang and T. Zha (2013): Land-price Dynamics and Macroeconomic Fluctuations, Econometrica 81, [29] Lubik, T. and F. Schorfheide (2003): Computing Sunspot Equilibria in Linear Rational Expectations Models, Journal of Economic Dynamics and Control 28, [30] Merton, R. (1948): The Self-ful lling Prophecy, The Antioch Review 8, [31] Nolan, C. and C. Thoenissen (2009): Financial Shocks and the US Business Cycle, Journal of Monetary Economics 56, [32] Otrok, C. (2001): On Measuring the Welfare Cost of Business Cycles, Journal of Monetary Economics 47, [33] Pavlov, O. and M. Weder (2017): Product Scope and Endogenous Fluctuations, Review of Economic Dynamics 24, [34] Pintus, P., Y. Wen and X. Xing (2016): The Inverted Leading Indicator Property and Redistribution E ect of the Interest Rate, Banque de France, mimeo. [35] Schmitt-Grohé, S. and M. Uribe (2012): What s News in Business Cycles?, Econometrica 80, [36] Weder, M. (2006): The Role of Preference Shocks and Capital Utilization in the Great Depression, International Economic Review 47, [37] Wen, Y. (1998): Capacity Utilization Under Increasing Returns To Scale, Journal of Economic Theory 81,

19 8 Appendix The not-to-be-published Appendix sets out the complete model, a discussion of the typical animal spirits cycle, conducts more robustness checks, and it lists the data sources and de nitions. We begin with collecting the model s equations. 8.1 Model equations and equilibrium dynamics The rst-order conditions for the household s optimization problems are 'N t = C t 1 W t t and C t A t r t = A t 0 u t 1 = E t (r t+1 u t+1 + A t+1 (1 t+1 )) : t C t+1 t+1 In the model, output, consumption, and real wage uctuate around the same stochastic growth trend Xt Y =( 1) = X t At, the growth rate of which is y t Xt Y =Xt Y 1 = x t ( a t ) 1. The trend in capital stock, which is also the trend in investment equals Xt K = Xt Y =A t, the growth rate of which is k t Xt K =Xt K 1 = x t ( a t ) 1 1. Besides, the government expenditure uctuates around its own trend Xt G. There is no growth trend in hours, utilization and marginal cost. We rst derive the detrended dynamic equilibrium equations and then log-linearly approximate them around the deterministic steady state. Let y t = Y t =Xt Y, c t = C t =Xt Y, w t = W t =Xt Y, i t = I t =Xt K, k t = K t =Xt K 1, g t = G t =Xt G, and y t =y approximately equal to Y t = Y t, where y represents the steady state of detrended output. The log-linearized system is summarized by ^y t = ^k t + ^u t ^ k t + (1 ) ^N t ^y t = [1 ^c t+1 = ^c t ^t [1 and ( k 1 + ) (1 + ) G Y ]^c t + (k 1 + ) ^{ t + G (1 + ) Y (^ag t + ^g t ) ^y t = (1 + ) ^N t + ^c t ^t ^t ^y t = (1 + )^u t + ^k t ^t ^ k t (1 ) ^k t+1 = (^k k t ^ k t ) + (k 1 + ) (1 + ) ^{ k t ^u k t (1 + ) ]^ k k t+1 + ^ (1 + ) t+1 + (^y k t+1 ^kt+1 + ^ t+1 ^u t+1 ) ^ t = ^y t + ^ t : In these equations, variables without time subscripts refer to steady state values while the hatted variables denote percent deviations from their corresponding steady-state, e.g., ^y t log(y t =y). 18

20 8.2 A Burns-Mitchell analysis of animal spirits We employ a classical method of business cycle analysis developed by Burns and Mitchell (1946) and Adelman and Adelman (1959) to evaluate the belief shock driven model in terms of whether it mimics the cyclical behavior of post war U.S. data. 12 A brief description of the idea follows. The business cycle series consist of a sequence of reference cycles, measured trough-to-trough by convention. We use NBER dates to determine the peak of the reference cycle for both U.S. and arti cially generated data. Our sample series includes eight complete trough-peak-trough cycles beginning in 1958:II and ending with the lower turning point in 2009:II. No prior ltering or detrending of the data has been undertaken that is we do not detrend the model output to allow for the presence of long-run technological progress and bring it in line with empirical data. Each complete reference cycle is divided into nine stages (I to IX). Stage I is the initial trough; stage V is the reference peak, and stage IX is the terminal trough. The expansion phase (stages I to V) is divided into three substages (II, III, and IV) of equal length (excluding time contained in stages I and V). The contraction phase (stages V to IX) is measured in an analogous fashion. Next, each observation in the cycle is expressed as a percentage of the cycle mean called cycle relatives. Mean cycle relatives per stage are averaged across all reference cycles to yield a graphical summary of an average business cycle in the nine-point-plot of Figure 10. The plot provides a visual impression of both the simulated data and the U.S. data. Concretely, Figure 7 displays the average behavior, in cycle relatives, over the nine stages of the business cycle for per capita real GDP and the arti cial equivalent when the model is counterfactually driven by belief shocks only. Stage I coincides with the initial trough, stage V with the peak, and stage IX corresponds to the terminal trough. The similar general shape of the two series demonstrates that arti cial series matches well postwar U.S. cycles. The per capita real GDP exhibits a distinct procyclical pattern, rising during expansions and falling during contractions. Both series peak in the same stage. Figure 7: Nine-point graph for U.S. GDP and counterfactually belief driven output 12 King and Plosser (1994) for a concise summary of the Burns-Mitchell procedure as well as its implementation in a general equilibrium context. 19

21 8.3 More robustness checks Justiniano, Primiceri and Tambalotti (2011) push for shocks that a ect the production of installed capital from investment goods or the transformation of savings into the future capital input. This is an alternative way of how to model exogenous nancial frictions. The idea of shocks to the marginal e ciency to investment (MEI) goes back to Greenwood, Hercowitz and Hu man (1988) who formulate the ideas as K t+1 = (1 t )K t + t I t where we abstract from adjustment costs to not mess with the indeterminacy properties of the arti cial economy. The shock t a ects the marginal e ciency of capital and it follows the process ln t = v ln t 1 + " t : The shock are likely a proxy for more fundamental disturbances to the functioning of the nancial sector. (Justiniano, Primiceri and Tambalotti, 2011). Again, we add a measurement error to the spread equation (to impose discipline on the inference of the MEI shock). Table 13 shows, in line with our previous ndings, that the animal spirits shocks remain the most prominent drivers of the U.S. business cycle. Table 14 shows the posterior means of the parameters in the model with transitory technology productivity. The estimated parameters are similar with that of the baseline estimation. 8.4 Bianchi and Nicolò (2017) We brie y set out the methodology that we apply. It closely follows Bianchi and Nicolò (2017) and it does not require to know the (analytical solution) of the boundaries of the determinacy region. The parameters of the loglinearized benchmark model are contained in the vector = [; ; y ; a ; k ; ; ; ; ; ; G=Y; x ; a ; ; g ; ; x ; a ; ; g ; ]: The linear rational expectations (LRE) model can be rewritten in the canonical form where 0()s t = 1 ()s t 1 + ()" t + () t ; (3) s t = [^y t ; ^c t ;^{ t ; ^N t ; ^k t ; ^u t ; ^ t ; E t [^y t+1 ]; E t [^c t+1 ]; E t [^ t+1 ]; E t [^u t+1 ]; ^ y t ; ^ a t ; ^ k t ; ^g t ; ^a g t ; ^ t ; ^ t ] 0 is a vector of endogenous variables, " t = [" x t ; " a t ; " t ; " g t ; " t ] 0 is a vector of exogenous shocks, and t = [ y t ; c t; t ; u t ] 0 collects the one-step ahead forecast errors for the expectational variables of the system. Since our model can generate at most one degree of indeterminacy, Bianchi and Nicolò suggest to append the original linear rational expectations model (3) with the autoregressive process! t = '! t 1 + t f;t (4) 20

22 where t is the sunspot shock and f;t can be any element of the forecast errors vector t. We choose f;t = y t. The variable ' belongs to the interval (-1,1) when the model is determinate or it is outside the unit circle under indeterminacy. Under determinacy the Blanchard-Kahn condition is satis ed and the absolute value of ' is inside the unit circle since the number of explosive roots of the original LRE model in (3) already equals the number of expectational variables in the model. Then the autoregressive process! t does not a ect the solution for the endogenous variables s t. On the other hand, under indeterminacy the Blanchard-Kahn condition is not satis ed. The system is characterized by one degree of indeterminacy and it is necessary to introduce another explosive root to ful ll the Blanchard-Kahn condition the absolute value of ' falls outside the unit circle. Denoting the newly-de ned vector of endogenous variables ^s t (s t ;! t ) 0 and the vector of exogenous shocks ^" t (" t ; t ) 0, then the system (3) and (4) can be condensed into ^0^s t = ^1^s t 1 + ^ ^" t + ^ t ; where and ^0 ^ 0() () ; ^1 1() 0 0 ' n () ; ^ f () 0 1 The matrix () in (3) is partitioned as () = [ n () f ()] without loss of generality. Figure 2 shows that our model has two determinacy regions and one indeterminacy region. During the mode- nding process, or MCMC, we encountered situations in which the estimation got stuck in one of these regions without crossing the boundaries, even though, in theory, the Metropolis-Hastings algorithm can explore the entire parameter space. Therefore, our estimation strategy sets di erent initial values (for each of the regions) while leaving the priors the same. Once we nd for each region a (local) mode, we start running the MCMC at each mode. Finally, we compare the three log data densities generated for each region. To start with, the prior probability of determinacy or indeterminacy is set. The priors are such that indeterminacy has the least prior probability so to err on the right side. All priors are as before but the prior for the elasticity of collateral is gamma-distributed with mean 0.5 and standard deviation 0.8 and the prior for the parameter ' follows a uniform distribution within [0,2]. Then, the prior probability for indeterminacy is 20 percent (a remaining prior probability falls to the source region, however, any draws from this regime are discarded). Following Bianchi and Nicolò (2017) the forecast error of output y t is the belief shock with variance 2, that is, the expectation error is correlated with the fundamental shocks and these correlations are estimated as in Farmer, Kharamov and Nicolò (2015). 8.5 Data description This appendix is to describe the details of the source and construction of the data used in estimation. The sample period covers the rst quarter of 1955 through the fourth quarter of 2014: 21 :